[tex]2 x^{2} -7x+5=0
[/tex]
a = 2
b = -7
c = 5
[tex]x = \frac{-b\pm\sqrt{b^2-4ac} }{2a}
[/tex]
[tex]x = \frac{7\pm\sqrt{49-4(2)(5)} }{2(2)}[/tex]
[tex]x = \frac{7\pm\sqrt{9} }{4}[/tex]
[tex]x = \frac{7\pm3 }{4}[/tex]
[tex]x_1 = \frac{7+3 }{4}=\frac{10}{4}=\boxed{\frac{5}{2}}[/tex]
[tex]x_2 = \frac{7-3 }{4}=\frac{4}{4}=\boxed{1}[/tex]
Check:
x = 5/2
[tex]2\frac{5}{2}^{2} -7\frac{5}{2}+5=0 [/tex]
[tex]2\frac{25}{4} -\frac{35}{2}+5=0 [/tex]
[tex]\frac{25}{2} -\frac{35}{2}+5=0 [/tex]
[tex]\frac{-10}{2}+5=0 [/tex]
[tex]-5+5=0 [/tex]
[tex]0=0 [/tex]
x = 1
[tex]2 (1)^{2} -7(1)+5=0 [/tex]
[tex]2-7+5=0 [/tex]
[tex]0=0 [/tex]
